TSTP Solution File: NUM845+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM845+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 14:31:00 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 12 unt; 0 nHn; 20 RR)
% Number of literals : 28 ( 0 equ; 12 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(vplus(u,v),vplus(v,u)),
file('NUM845+2.p',unknown),
[] ).
cnf(5,axiom,
equal(vplus(u,vsucc(v)),vsucc(vplus(u,v))),
file('NUM845+2.p',unknown),
[] ).
cnf(6,axiom,
equal(vplus(vmul(vd411,skc1),skc1),vmul(vsucc(vd411),skc1)),
file('NUM845+2.p',unknown),
[] ).
cnf(8,axiom,
equal(vplus(vmul(u,v),u),vmul(u,vsucc(v))),
file('NUM845+2.p',unknown),
[] ).
cnf(9,axiom,
equal(vplus(vplus(u,v),w),vplus(u,vplus(v,w))),
file('NUM845+2.p',unknown),
[] ).
cnf(10,axiom,
~ equal(vplus(vmul(vd411,vsucc(skc1)),vsucc(skc1)),vmul(vsucc(vd411),vsucc(skc1))),
file('NUM845+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(vplus(vmul(vd411,u),u),vmul(vsucc(vd411),u))
| equal(vplus(vplus(vmul(vd411,u),u),vsucc(vd411)),vplus(vmul(vsucc(vd411),u),vsucc(vd411))) ),
file('NUM845+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(vplus(vmul(vd411,u),u),vmul(vsucc(vd411),u))
| equal(vplus(vplus(vmul(vd411,u),vd411),vsucc(u)),vplus(vmul(vd411,vsucc(u)),vsucc(u))) ),
file('NUM845+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ equal(vplus(vmul(vd411,u),u),vmul(vsucc(vd411),u))
| equal(vplus(vmul(vd411,u),vplus(u,vsucc(vd411))),vplus(vmul(vd411,u),vplus(vsucc(vd411),u))) ),
file('NUM845+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(vplus(vmul(vd411,u),u),vmul(vsucc(vd411),u))
| equal(vplus(vmul(vd411,u),vplus(vsucc(vd411),u)),vplus(vmul(vd411,u),vsucc(vplus(vd411,u)))) ),
file('NUM845+2.p',unknown),
[] ).
cnf(19,plain,
equal(vplus(u,vmul(u,v)),vmul(u,vsucc(v))),
inference(rew,[status(thm),theory(equality)],[4,8]),
[iquote('0:Rew:4.0,8.0')] ).
cnf(20,plain,
equal(vplus(skc1,vmul(vd411,skc1)),vmul(vsucc(vd411),skc1)),
inference(rew,[status(thm),theory(equality)],[4,6]),
[iquote('0:Rew:4.0,6.0')] ).
cnf(21,plain,
~ equal(vplus(vsucc(skc1),vmul(vd411,vsucc(skc1))),vmul(vsucc(vd411),vsucc(skc1))),
inference(rew,[status(thm),theory(equality)],[4,10]),
[iquote('0:Rew:4.0,10.0')] ).
cnf(23,plain,
( ~ equal(vplus(u,vmul(vd411,u)),vmul(vsucc(vd411),u))
| equal(vsucc(vplus(vmul(vd411,u),vplus(u,vd411))),vmul(vsucc(vd411),vsucc(u))) ),
inference(rew,[status(thm),theory(equality)],[5,12,9,19,4]),
[iquote('0:Rew:5.0,12.1,5.0,12.1,9.0,12.1,19.0,12.1,4.0,12.1,4.0,12.0')] ).
cnf(24,plain,
( ~ equal(vplus(u,vmul(vd411,u)),vmul(vsucc(vd411),u))
| equal(vsucc(vplus(vmul(vd411,u),vplus(vd411,u))),vplus(vsucc(u),vmul(vd411,vsucc(u)))) ),
inference(rew,[status(thm),theory(equality)],[5,13,9,4]),
[iquote('0:Rew:5.0,13.1,5.0,13.1,9.0,13.1,4.0,13.1,4.0,13.0')] ).
cnf(25,plain,
( ~ equal(vplus(u,vmul(vd411,u)),vmul(vsucc(vd411),u))
| equal(vplus(vmul(vd411,u),vplus(vsucc(vd411),u)),vmul(vsucc(vd411),vsucc(u))) ),
inference(rew,[status(thm),theory(equality)],[23,15,5,4]),
[iquote('0:Rew:23.1,15.1,5.0,15.1,5.0,15.1,4.0,15.0')] ).
cnf(26,plain,
( ~ equal(vplus(u,vmul(vd411,u)),vmul(vsucc(vd411),u))
| equal(vplus(vsucc(u),vmul(vd411,vsucc(u))),vmul(vsucc(vd411),vsucc(u))) ),
inference(rew,[status(thm),theory(equality)],[25,16,24,5,4]),
[iquote('0:Rew:25.1,16.1,24.1,16.1,5.0,16.1,4.0,16.0')] ).
cnf(33,plain,
~ equal(vplus(skc1,vmul(vd411,skc1)),vmul(vsucc(vd411),skc1)),
inference(res,[status(thm),theory(equality)],[26,21]),
[iquote('0:Res:26.1,21.0')] ).
cnf(34,plain,
~ equal(vmul(vsucc(vd411),skc1),vmul(vsucc(vd411),skc1)),
inference(rew,[status(thm),theory(equality)],[20,33]),
[iquote('0:Rew:20.0,33.0')] ).
cnf(35,plain,
$false,
inference(obv,[status(thm),theory(equality)],[34]),
[iquote('0:Obv:34.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM845+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 03:35:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 15 clauses.
% 0.20/0.44 SPASS allocated 85138 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.00 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 1, length 20 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ qu_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_3_a41__a44__a32_and_a40_holds_a40_definiens_a40_29_a41__a44__a32_45_a44__a32_0_a41__a44__a32_holds_a40_definiens_a40_29_a41__a44__a32_44_a44__a32_0_a41__a41__a41_ qu_a40_ind_a40_267_a41__a44__a32_imp_a40_267_a41__a41_ qu_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_32_a41__a44__a32_and_a40_holds_a40_definiens_a40_249_a41__a44__a32_399_a44__a32_0_a41__a44__a32_holds_a40_definiens_a40_249_a41__a44__a32_398_a44__a32_0_a41__a41__a41_ ass_a40_cond_a40_33_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_conseq_a40_263_a41__a44__a32_1_a41__a44__a32_6_a41_ ass_a40_cond_a40_conseq_a40_263_a41__a44__a32_1_a41__a44__a32_0_a41_ ass_a40_cond_a40_conseq_a40_263_a41__a44__a32_1_a41__a44__a32_4_a41_ ass_a40_cond_a40_conseq_a40_263_a41__a44__a32_1_a41__a44__a32_3_a41_
% 0.20/0.44
%------------------------------------------------------------------------------